The analysis of earthquake stability of slopes is one of the most important research subjects in geotechnical engineering and earthquake engineering. Two different concepts of slope earthquake stability are put forward in this paper. One concept is the so-called strength reserve stability. The other is named as the dynamic overloading stability. The first concept of slope earthquake stability has been widely accepted. Its relative analysis methods are also well developed. The second one, however, is seldom mentioned till now. Its failure criterion and analysis method are yet to be explored. This paper investigates the failure criterion and the analysis method of dynamic overloading earthquake stability. The dynamic overloading earthquake stability of a loess slope at Panlongyuan in Baoji, Shaanxi Province, China is analyzed with the load increasing method proposed in this paper. The result reveals that the dynamic overloading earthquake stability of the slope is quite high to the action of the earthquake ground motion with exceeding probability 10% in coming 50 years.